To increase the transmission capacity and spectral efficiency of wireless or wired communication, various standards have proposed MIMO transmission schemes that use an array of transmit and receive antennas or lines to carry multiple independent spatial streams simultaneously and in the same bandwidth. Each of the separate transmit signals may be detected jointly from a set of receive signals using an optimal maximum likelihood (ML) detection scheme; however, the complexity of a complete exhaustive search ML detection method tends to increase exponentially with the number of spatial streams and the size of the signal constellation. As such, some implementations may limit MIMO detection to a sub-optimal search over a space of possible solutions that may require fewer computations but also may result in lower performance.
Example sub-optimal MIMO detection algorithms include linear zero-forcing (ZF) and minimum mean-squared-error (MMSE) receivers that may multiply the receive signals by an inverse of the channel response to cancel the interference effect of the channel, thereby extracting the separate transmit signals from the composite receive signals. While more computationally efficient than ML detection, such algorithms may amplify the additive noise reducing the performance of the system. Another sub-optimal MIMO algorithm may use non-linear decision feedback detection to decide each of the transmitted signals sequentially, thereby cancelling the interference of each detected transmit symbol successively from the composite received signal; however, incorrect decisions may propagate through the detection process resulting again in reduced performance.
Another sub-optimal non-linear detection algorithm, known as K-best sphere decoding, may perform a non-exhaustive search for the transmitted signal by limiting the number of candidate solutions kept after each stage of a multiple stage search. For each stage, K candidate solutions resulting from the previous stage may be extended to K*M candidate solutions, where M may equal the size of the signal constellation, and a cumulative metric may be calculated for each of the resulting K*M candidate solutions. The K*M candidate solutions may then be sorted by the cumulative metric, with only the “best” K candidate solutions retained for the next stage of calculation. While the number of total computations for non-exhaustive K-best sphere decoding may grow more slowly than exhaustive ML detection, the sorting process may require significant memory and may lack parallelism to speed the operation in chip implementations.
In addition to a hard decision detection result, i.e. a “best” estimate of the transmit symbols, wireless MIMO communication systems may use error correction codes requiring a soft decision reliability metric for each bit of the estimated transmit symbols. Because the K-best sphere decoding algorithm limits the search space, the set of candidate solutions at the final stage may not contain candidates for each possible bit value (0 or 1) in the set of estimated transmit symbols needed for a soft decision reliability metric to input to a subsequent error correction decoder.
Thus, there exists a need for a reduced complexity maximum likelihood MIMO detection scheme that may provide near optimal performance, may parallelize for efficient implementation, and may provide both hard decision and soft decision results for a wireless MIMO communication system. Similarly, there is a need for such schemes that may employ readily implemented QR decomposition functions.